Question

In the given figure, $PQRS$ is a cyclic trapezium in which $PQ\parallel SR$. If $\angle$P = 82${}^o$, then $\angle$S is:

• A. ${98}^o$
• B. ${108}^o$
• C. Data not sufficient
• D. None of these

Answer 1

Answer: (A)

${98}^o$

Given, $PQRS$ is a cyclic trapezium with $PQ\parallel SR,\angle QPS={82}^o.$

Now, $\angle QPS+\angle RSP={180}^o$ ...[ Since the sum of co-interior anglesis $={180}^o$].

$\therefore \angle RSP={180}^o-\angle QPS={180}^o-{82}^o={98}^o.$

Hence, option $A$ is correct.